We discuss the no-ghost theorem in the massive gravity in a covariant manner.
Using the BRST formalism and St\"{u}ckelberg fields, we first clarify how the
Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli
mass term. Here we find that the crucial point in the proof is that there is no
higher (time) derivative for the St\"{u}ckelberg `scalar' field. We then
analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and
Tolley, and show that there is no ghost for general admissible backgrounds. In
this process, we find a very nontrivial decoupling limit for general
backgrounds. We end the paper by demonstrating the general results explicitly
in a nontrivial example where there apparently appear higher time derivatives
for St\"{u}ckelberg scalar field, but show that this does not introduce the
ghost into the theory.Comment: 24 page
